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Continuous Time Random Walk: Difference between revisions
→The Master Equation
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:<math>\frac{\partial n(x,t)}{\partial t} = \int_0^t \left ( \int_{-\infty}^{\infty}{K(x-x',t-t',x',t')n(x',t')dx'} - n(x,t')\int_{-\infty}^{\infty}{K(x-x',t-t',x',t')dx'}\right )dt'</math> | :<math>\frac{\partial n(x,t)}{\partial t} = \int_0^t \left ( \int_{-\infty}^{\infty}{K(x-x',t-t',x',t')n(x',t')dx'} - n(x,t')\int_{-\infty}^{\infty}{K(x-x',t-t',x',t')dx'}\right )dt'</math> | ||
where ''n'' is the particle (probability) density, and ''K'' a kernel | where ''n'' is the particle (probability) density, and ''K'' a kernel of the form | ||
:<math>K( \Delta x, \Delta t; x,t) = p(\Delta x; x,t+\Delta t) \phi(\Delta t; x)</math> | |||
== Fractional Differential Equations == | == Fractional Differential Equations == | ||